Question

two concentric circles are of radii 6cm and 4cm with centre O .if AP is a tangent to the larger circle and BP to the smaller circle and length of AP is 8cm ,find the length of BP​

Answer 1

PB = 9.165 cm.

Step-by-step explanation:

Given:

As shown in the figure AP = 8 cm, OA= 6 cm , OB = 4 cm

It is known to us that the radius is perpendicular to the tangent at the point of contact.

∠PAO = ∠PBO = 90°

In  POA,

$OP^2=OA^2+AP^2$

$OP=\sqrt{OA+AP}$

$OP=\sqrt{36+64}$

$OP=\sqrt{100}$

OP = 10 cm.    

In  POB,

$OP^2 = BO^2 + PB^2$

$100 - 16= PB^2$

$PB =\sqrt{84}$

PB = 9.165 cm.

Answer 2

The length of BP will be 2√21

1.given AP is tangent of larger circle and BP is tangent of smaller circle

AP=8cm

2.let centre be O

OP=√AO²+AP²

AO=6cm

3.OP=10cm

Length of tangent to smaller circle=√OP²-OB²=√84

=2√21